What you read in the papers re. sun signs is for the most part not true astrology.
True astrology is complex and is based on the minute of birth, as well as the aspects of the planets in relationship to each other. depending on their place in the sky at that time. the main three or four markers for personality are:
- The rising (ascendant) sign (different to the sun sign and changes every hour or so). Within each rising sign there are a number of "bounds" or smaller divisions, changing every few minutes, each ruled by a different planet, again making a further impact on the individual horoscope
- The moon sign (the moon changes sign every 3 days)
- the sun sign
... and many more elements
These all work together to give a bigger picture of the life path etc and indicate what kind of challenges the person might face.
Additionally to this there are the position of the other planets (Mars, venus, saturn etc) each with their own unique meanings. Each is dignified or in detriment or similar in different places of the chart and will denote a different aspect of our character. For example, Mars in venus's sign or house will behave completely differently to when it is in its own sign / house. Someone with a strong mars (such as Trump) might be more blustery or prone to outbursts, for example.
The rising sign denotes the astrological "houses" or places, of which there are 12, each denoting a life area e.g. money, career, children etc. The meanings of the houses are more complex than this. Each planet will fall into a house, and have meaning for that area of life, positive, negative or neutral.
Astrologers can then map the current planetary positions against the birth chart to get an idea of what kind of "weather" might be coming up.
Most astrologers don't believe "rocks in the sky" exert an influence on people, but they are astrological omens, divinitory in nature and rather than being the cause of the events in someone's life, are indicators of what is coming up. Astrology in that sense is strongly linked to belief in god or the sacred / divine as well as to some extent fate, but most astrologers believe we have free will within this.